Subgroups — #13035908

Order 1280.

714 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10617110	C₂	1	1	yes	maximal, characteristic
2	#10617106	C₂	1	1	yes	maximal, characteristic
3	D₅×#433	C₂	1	1	yes	maximal, characteristic
4	#10604038	C₂	1	1	yes	maximal, characteristic, complemented
5	#10604038	C₂	1	1	yes	maximal, characteristic, complemented
6	#10604037	C₂	1	1	yes	maximal, characteristic, complemented
7	#10604036	C₂	1	1	yes	maximal, characteristic, complemented
8	#10603918	C₂	1	1	yes	maximal, characteristic
9	#10603918	C₂	1	1	yes	maximal, characteristic
10	#10603917	C₂	1	1	yes	maximal, characteristic
11	#10603916	C₂	1	1	yes	maximal, characteristic
12	#10603888	C₂	1	1	yes	maximal, characteristic, complemented
13	#10603888	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#3996	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#3995	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₅⋊M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×#700	C₂²	1	1	yes	characteristic
18	D₅×#117	C₂²	1	1	yes	characteristic
19	#65756	C₂²	1	1	yes	characteristic
20	#65756	C₂²	1	1	yes	characteristic
21	C₂×#3996	C₂²	1	1	yes	characteristic
22	C₂×#3996	C₂²	1	1	yes	characteristic
23	C₂×#3996	C₂²	1	1	yes	characteristic
24	C₂×#3996	C₂²	1	1	yes	characteristic
25	C₂×#3995	C₂²	1	1	yes	characteristic
26	C₂×#3995	C₂²	1	1	yes	characteristic
27	C₂×#3995	C₂²	1	1	yes	characteristic
28	C₂×#3995	C₂²	1	1	yes	characteristic
29	#65706	—	2	1	no	—
30	#65706	—	2	1	no	—
31	#65701	—	2	1	no	—
32	#65701	—	2	1	no	—
33	#65697	—	2	1	no	—
34	#65697	—	2	1	no	—
35	#65691	—	2	1	no	—
36	#65691	—	2	1	no	—
37	#65682	C₂²	1	1	yes	characteristic
38	#65681	C₂²	1	1	yes	characteristic
39	C₄×#700	C₂²	1	1	yes	characteristic
40	C₄×#700	C₂²	1	1	yes	characteristic
41	C₄×#700	C₂²	1	1	yes	characteristic
42	C₄×#700	C₂²	1	1	yes	characteristic
43	C₄×#700	C₂²	1	1	yes	characteristic
44	C₄×#700	C₂²	1	1	yes	characteristic
45	C₅×#433	C₄	1	1	yes	characteristic
46	#65289	C₄	1	1	yes	characteristic
47	#65129	C₄	1	1	yes	characteristic
48	#65129	C₄	1	1	yes	characteristic
49	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	D₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	D₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
53	#65009	C₄	1	1	yes	characteristic
54	#65009	C₄	1	1	yes	characteristic
55	#64998	C₄	1	1	yes	characteristic
56	D₅×#97	C₂²	1	1	yes	characteristic
57	#64979	C₄	1	1	yes	characteristic
58	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
59	#64896	C₂²	1	1	yes	characteristic
60	#64896	C₂²	1	1	yes	characteristic
61	#64896	C₂²	1	1	yes	characteristic
62	#64896	C₂²	1	1	yes	characteristic
63	#64896	C₂²	1	1	yes	characteristic
64	#64896	C₂²	1	1	yes	characteristic
65	#64896	C₂²	1	1	yes	characteristic
66	#64896	C₂²	1	1	yes	characteristic
67	#21372	—	5	1	no	maximal, Sylow
68	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
69	C₂×#704	—	2	1	no	—
70	C₂²×#170	—	2	1	no	—
71	D₅⋊M₁₆	—	2	2	no	—
72	D₅⋊M₁₆	—	2	2	no	—
73	C₂×#700	—	2	1	no	—
74	C₂×#700	—	2	2	no	—
75	C₂×#700	—	2	2	no	—
76	C₂×#700	C₂³	1	1	yes	characteristic
77	C₂×#700	C₂³	1	1	yes	characteristic
78	C₂×#700	C₂³	1	1	yes	characteristic
79	C₂×#700	C₂³	1	1	yes	characteristic
80	C₂×#700	C₂³	1	1	yes	characteristic
81	C₂×#700	C₂³	1	1	yes	characteristic
82	C₂×#700	C₂³	1	1	yes	characteristic
83	C₂×#700	C₂³	1	1	yes	characteristic
84	C₂×D₅⋊C₈	—	2	1	no	—
85	C₅×#117	C₂×C₄	1	1	yes	characteristic
86	#4072	C₂×C₄	1	1	yes	characteristic
87	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
88	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
89	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
90	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
91	#4038	D₄	1	1	yes	characteristic
92	#4038	D₄	1	1	yes	characteristic
93	D₅×C₄⋊C₄	Q₈	1	1	yes	characteristic
94	D₅×C₄⋊C₄	Q₈	1	1	yes	characteristic
95	D₅×C₂²⋊C₄	Q₈	1	1	yes	characteristic
96	D₅×C₂²⋊C₄	Q₈	1	1	yes	characteristic
97	#4023	D₄	1	1	yes	characteristic
98	#4023	D₄	1	1	yes	characteristic
99	#4018	C₂×C₄	1	1	yes	characteristic
100	#4018	C₂×C₄	1	1	yes	characteristic
101	C₄²×D₅	C₂³	1	1	yes	characteristic
102	C₄²×D₅	C₂³	1	1	yes	characteristic
103	C₂²⋊#170	—	2	1	no	—
104	C₂²⋊#170	—	2	1	no	—
105	#4004	—	2	1	no	—
106	#4004	—	2	1	no	—
107	#4003	—	2	1	no	—
108	#4003	—	2	1	no	—
109	#4002	—	2	1	no	—
110	#4002	—	2	1	no	—
111	#4002	—	2	1	no	—
112	#4002	—	2	1	no	—
113	#4002	—	2	1	no	—
114	#4002	—	2	1	no	—
115	C₄⋊#170	—	2	1	no	—
116	C₄⋊#170	—	2	1	no	—
117	C₄×#170	—	2	1	no	—
118	C₄×#170	—	2	1	no	—
119	C₄×#170	—	2	1	no	—
120	C₄×#170	—	2	1	no	—
121	C₄×#170	—	2	1	no	—
122	C₄×#170	—	2	1	no	—
123	#3996	—	2	2	no	—
124	#3996	—	2	2	no	—
125	#3996	—	2	2	no	—
126	#3996	—	2	2	no	—
127	#3995	—	2	2	no	—
128	#3995	—	2	2	no	—
129	#3995	—	2	2	no	—
130	#3995	—	2	2	no	—
131	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
132	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
133	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
134	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
135	C₅×#97	C₂×C₄	1	1	yes	characteristic
136	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
137	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
138	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
139	#3952	C₂×C₄	1	1	yes	characteristic
140	#3952	C₂×C₄	1	1	yes	characteristic
141	#3952	C₂×C₄	1	1	yes	characteristic
142	#3952	C₂×C₄	1	1	yes	characteristic
143	#3947	C₂×C₄	1	1	yes	characteristic
144	#3947	C₂×C₄	1	1	yes	characteristic
145	#3946	C₂×C₄	1	1	yes	characteristic
146	#3946	C₂×C₄	1	1	yes	characteristic
147	#3946	C₂×C₄	1	1	yes	characteristic
148	#3946	C₂×C₄	1	1	yes	characteristic
149	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
150	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
151	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
152	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
153	#3935	C₂×C₄	1	1	yes	characteristic
154	C₄×#168	C₂×C₄	1	1	yes	characteristic
155	#2921	—	5	1	no	—
156	C₂×#433	—	5	1	no	—
157	#2873	—	5	1	no	—
158	#1950	—	5	1	no	—
159	#1950	—	5	1	no	—
160	#1950	—	5	1	no	—
161	#1950	—	5	1	no	—
162	#1855	—	5	1	no	—
163	#1855	—	5	1	no	—
164	#1855	—	5	1	no	—
165	#1855	—	5	1	no	—
166	#1778	—	5	1	no	—
167	#1778	—	5	1	no	—
168	C₄×#108	—	5	1	no	—
169	C₄×#108	—	5	1	no	—
170	C₂³×D₅	C₂×Q₈	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
172	C₂²×Dic₅	C₂×D₄	1	1	yes	characteristic
173	C₂×C₄×D₅	—	2	1	no	—
174	C₂×C₄×D₅	—	2	1	no	—
175	C₂×C₄×D₅	—	2	1	no	—
176	C₂×C₄×D₅	—	2	1	no	—
177	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
179	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
180	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
181	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
182	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
183	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
184	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
185	#704	—	2	4	no	—
186	C₂×#170	—	2	4	no	—
187	C₂×#170	—	2	1	no	—
188	C₂×#170	—	2	1	no	—
189	C₂×#170	—	2	1	no	—
190	C₂×#170	—	2	1	no	—
191	C₂×#170	—	2	1	no	—
192	C₂×#170	—	2	1	no	—
193	C₂×#170	—	2	1	no	—
194	C₂×#170	—	2	1	no	—
195	#700	—	2	4	no	—
196	#700	—	2	1	no	—
197	#700	—	2	1	no	—
198	#700	—	2	1	no	—
199	#700	—	2	1	no	—
200	#700	—	2	1	no	—
201	#700	—	2	1	no	—
202	#700	—	2	1	no	—
203	#700	—	2	1	no	—
204	#700	—	2	1	no	—
205	#700	—	2	1	no	—
206	#700	—	2	1	no	—
207	#700	—	2	1	no	—
208	#700	#41	1	2	yes	—
209	#700	#41	1	2	yes	—
210	#700	#41	1	2	yes	—
211	#700	#41	1	2	yes	—
212	D₅⋊C₈	—	2	4	no	—
213	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
214	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
215	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
217	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
218	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
219	C₅×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
220	C₅×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
221	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
222	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
223	C₂²⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
224	C₂²⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
225	#685	C₄⋊C₄	1	1	yes	characteristic
226	#685	C₄⋊C₄	1	1	yes	characteristic
227	#685	C₄⋊C₄	1	1	yes	characteristic
228	#685	C₄⋊C₄	1	1	yes	characteristic
229	C₄⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
230	C₄⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
231	#683	C₄⋊C₄	1	1	yes	characteristic
232	#683	C₄⋊C₄	1	1	yes	characteristic
233	#683	C₄⋊C₄	1	1	yes	characteristic
234	#683	C₄⋊C₄	1	1	yes	characteristic
235	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
236	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
237	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
238	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
239	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
240	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
241	C₂×#168	C₂²×C₄	1	1	yes	characteristic
242	C₂×#168	C₂²×C₄	1	1	yes	characteristic
243	C₂×#168	C₂²×C₄	1	1	yes	characteristic
244	C₂×#168	C₂²×C₄	1	1	yes	characteristic
245	C₈×D₅	—	2	1	no	—
246	C₈×D₅	—	2	1	no	—
247	C₈×D₅	—	2	1	no	—
248	C₈×D₅	—	2	1	no	—
249	C₈×D₅	—	2	1	no	—
250	C₈×D₅	—	2	1	no	—
251	C₈×D₅	—	2	1	no	—
252	C₈×D₅	—	2	1	no	—
253	C₂²×M₁₆	—	5	1	no	—
254	C₂²×M₁₆	—	5	1	no	—
255	C₂×#117	—	5	1	no	—
256	#433	—	5	1	no	—
257	#433	—	5	1	no	—
258	#433	—	5	1	no	—
259	#433	—	5	1	no	—
260	#433	—	5	1	no	—
261	#433	—	5	1	no	—
262	#433	—	5	1	no	—
263	#433	—	10	1	no	—
264	#433	—	10	1	no	—
265	#433	—	10	1	no	—
266	#433	—	10	1	no	—
267	#433	AGL(1,𝔽₅)	1	1	yes	characteristic
268	C₂×#108	—	5	1	no	—
269	C₂×#108	—	5	1	no	—
270	C₂×#108	—	5	1	no	—
271	C₂×#108	—	5	1	no	—
272	C₂×#108	—	5	1	no	—
273	C₂×#108	—	5	1	no	—
274	C₂×#108	—	5	1	no	—
275	C₂×#108	—	5	1	no	—
276	#423	—	5	1	no	—
277	#423	—	5	1	no	—
278	C₂×C₄⋊C₈	—	5	1	no	—
279	C₂×C₄⋊C₈	—	5	1	no	—
280	#407	—	5	1	no	—
281	#407	—	5	1	no	—
282	C₂×C₂²⋊C₈	—	5	1	no	—
283	C₂×C₂²⋊C₈	—	5	1	no	—
284	#405	—	10	1	no	—
285	#405	—	10	1	no	—
286	#405	—	10	1	no	—
287	#405	—	10	1	no	—
288	C₄×M₁₆	—	5	1	no	—
289	C₄×M₁₆	—	5	1	no	—
290	C₄×M₁₆	—	5	1	no	—
291	C₄×M₁₆	—	5	1	no	—
292	C₄×M₁₆	—	5	1	no	—
293	C₄×M₁₆	—	5	1	no	—
294	C₂×#97	—	5	1	no	—
295	C₂×C₄×C₈	—	5	1	no	—
296	#341	—	5	1	no	—
297	#341	—	5	1	no	—
298	#341	—	5	1	no	—
299	#341	—	5	1	no	—
300	#341	—	5	1	no	—
301	#341	—	5	1	no	—
302	#341	—	5	1	no	—
303	#341	—	5	1	no	—
304	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
305	C₂²×D₅	—	2	1	no	—
306	C₂²×D₅	—	2	1	no	—
307	C₂²×D₅	—	4	1	no	—
308	C₂²×D₅	—	4	1	no	—
309	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
310	C₂²×D₅	C₂²×Q₈	1	1	yes	characteristic
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
314	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
317	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
318	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
319	C₂×Dic₅	—	2	1	no	—
320	C₂×Dic₅	—	2	1	no	—
321	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
322	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
323	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
324	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
325	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
326	C₂×Dic₅	C₂²×D₄	1	1	yes	characteristic
327	C₄×D₅	—	2	1	no	—
328	C₄×D₅	—	2	1	no	—
329	C₄×D₅	—	2	1	no	—
330	C₄×D₅	—	2	1	no	—
331	C₄×D₅	—	2	1	no	—
332	C₄×D₅	—	2	1	no	—
333	C₄×D₅	—	4	1	no	—
334	C₄×D₅	—	4	1	no	—
335	C₄×D₅	—	4	1	no	—
336	C₄×D₅	—	4	1	no	—
337	C₄×D₅	C₂×#41	1	1	yes	characteristic
338	C₄×D₅	C₂×#41	1	1	yes	characteristic
339	C₄×D₅	C₂×#41	1	1	yes	characteristic
340	C₄×D₅	C₂×#41	1	1	yes	characteristic
341	#170	—	2	2	no	—
342	#170	—	2	2	no	—
343	#170	—	2	2	no	—
344	#170	—	2	2	no	—
345	#170	—	4	1	no	—
346	#170	—	4	1	no	—
347	#170	—	4	1	no	—
348	#170	—	4	1	no	—
349	C₅×C₈	—	2	1	no	—
350	C₅×C₈	—	2	1	no	—
351	C₅×C₈	—	2	1	no	—
352	C₅×C₈	—	2	1	no	—
353	#168	—	2	1	no	—
354	#168	—	2	1	no	—
355	#168	—	2	1	no	—
356	#168	—	2	1	no	—
357	C₂³×C₄	—	5	1	no	—
358	C₂×M₁₆	—	5	1	no	—
359	C₂×M₁₆	—	5	1	no	—
360	C₂×M₁₆	—	5	1	no	—
361	C₂×M₁₆	—	5	1	no	—
362	C₂×M₁₆	—	5	1	no	—
363	C₂×M₁₆	—	5	1	no	—
364	C₂×M₁₆	—	5	1	no	—
365	C₂×M₁₆	—	5	1	no	—
366	C₂×M₁₆	—	10	2	no	—
367	C₂×M₁₆	—	10	2	no	—
368	C₂×M₁₆	—	10	2	no	—
369	C₂×M₁₆	—	10	2	no	—
370	C₂×M₁₆	—	10	1	no	—
371	C₂×M₁₆	—	10	1	no	—
372	C₂²×C₈	—	5	1	no	—
373	C₂²×C₈	—	5	1	no	—
374	C₂²×C₈	—	5	1	no	—
375	C₂²×C₈	—	5	1	no	—
376	C₂²×C₈	—	10	1	no	—
377	C₂²×C₈	—	10	1	no	—
378	#117	—	5	1	no	—
379	#117	—	5	1	no	—
380	#117	—	5	1	no	—
381	#117	—	5	1	no	—
382	#117	—	5	1	no	—
383	#117	—	5	1	no	—
384	#117	—	5	1	no	—
385	#117	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
386	C₂×C₄⋊C₄	—	5	1	no	—
387	C₂×C₄⋊C₄	—	5	1	no	—
388	C₂×C₂²⋊C₄	—	5	1	no	—
389	C₂×C₂²⋊C₄	—	5	1	no	—
390	C₂×C₄²	—	5	1	no	—
391	C₂×C₄²	—	5	1	no	—
392	#108	—	10	2	no	—
393	#108	—	10	2	no	—
394	#108	—	10	2	no	—
395	#108	—	10	2	no	—
396	#108	—	10	2	no	—
397	#108	—	10	2	no	—
398	#108	—	10	2	no	—
399	#108	—	10	2	no	—
400	C₄⋊C₈	—	5	1	no	—
401	C₄⋊C₈	—	5	1	no	—
402	C₄⋊C₈	—	5	1	no	—
403	C₄⋊C₈	—	5	1	no	—
404	C₄⋊C₈	—	5	1	no	—
405	C₄⋊C₈	—	5	1	no	—
406	C₄⋊C₈	—	10	1	no	—
407	C₄⋊C₈	—	10	1	no	—
408	C₄⋊C₈	—	10	1	no	—
409	C₄⋊C₈	—	10	1	no	—
410	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
411	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
412	C₂²⋊C₈	—	5	1	no	—
413	C₂²⋊C₈	—	5	1	no	—
414	C₂²⋊C₈	—	5	1	no	—
415	C₂²⋊C₈	—	5	1	no	—
416	C₂²⋊C₈	—	5	1	no	—
417	C₂²⋊C₈	—	5	1	no	—
418	C₂²⋊C₈	—	10	1	no	—
419	C₂²⋊C₈	—	10	1	no	—
420	C₂²⋊C₈	—	10	1	no	—
421	C₂²⋊C₈	—	10	1	no	—
422	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
423	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
424	#97	—	5	1	no	—
425	#97	—	5	1	no	—
426	#97	—	5	1	no	—
427	#97	—	10	1	no	—
428	#97	—	10	1	no	—
429	#97	—	10	1	no	—
430	#97	—	10	1	no	—
431	#97	—	10	1	no	—
432	#97	—	10	1	no	—
433	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
434	C₄×C₈	—	5	1	no	—
435	C₄×C₈	—	5	1	no	—
436	C₄×C₈	—	5	1	no	—
437	C₄×C₈	—	10	1	no	—
438	C₄×C₈	—	10	1	no	—
439	C₄×C₈	—	10	1	no	—
440	C₄×C₈	—	10	1	no	—
441	C₄×C₈	—	10	1	no	—
442	C₄×C₈	—	10	1	no	—
443	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
444	C₂²×C₅	—	2	1	no	—
445	C₂²×C₅	—	2	1	no	—
446	C₂²×C₅	—	2	1	no	—
447	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
448	C₂×D₅	—	2	1	no	—
449	C₂×D₅	—	2	1	no	—
450	C₂×D₅	—	2	1	no	—
451	C₂×D₅	—	2	1	no	—
452	C₂×D₅	—	2	1	no	—
453	C₂×D₅	—	8	1	no	—
454	C₂×D₅	—	8	1	no	—
455	C₂×D₅	#533	1	1	yes	characteristic
456	C₂×D₅	#533	1	1	yes	characteristic
457	C₄×C₅	—	2	1	no	—
458	C₄×C₅	—	2	1	no	—
459	C₄×C₅	—	2	1	no	—
460	C₄×C₅	—	2	1	no	—
461	C₄×C₅	—	2	1	no	—
462	C₄×C₅	C₄×#41	1	1	yes	characteristic
463	C₄×C₅	C₄×#41	1	1	yes	characteristic
464	Dic₅	—	2	1	no	—
465	Dic₅	—	2	1	no	—
466	Dic₅	—	2	1	no	—
467	Dic₅	—	2	1	no	—
468	Dic₅	—	2	1	no	—
469	Dic₅	#525	1	1	yes	characteristic
470	Dic₅	#525	1	1	yes	characteristic
471	C₂⁴	—	5	1	no	—
472	C₂²×C₄	—	5	1	no	—
473	C₂²×C₄	—	5	1	no	—
474	C₂²×C₄	—	5	1	no	—
475	C₂²×C₄	—	5	1	no	—
476	C₂²×C₄	—	5	1	no	—
477	C₂²×C₄	—	5	1	no	—
478	C₂²×C₄	—	5	1	no	—
479	C₂²×C₄	—	5	1	no	—
480	C₂²×C₄	—	5	1	no	—
481	C₂²×C₄	—	10	1	no	—
482	C₂²×C₄	—	10	1	no	—
483	C₂²×C₄	—	10	1	no	—
484	C₂²×C₄	—	10	1	no	—
485	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
486	M₁₆	—	5	2	no	—
487	M₁₆	—	5	2	no	—
488	M₁₆	—	5	2	no	—
489	M₁₆	—	5	2	no	—
490	M₁₆	—	10	1	no	—
491	M₁₆	—	10	1	no	—
492	M₁₆	—	10	1	no	—
493	M₁₆	—	10	1	no	—
494	M₁₆	—	10	4	no	—
495	M₁₆	—	10	4	no	—
496	M₁₆	—	10	1	no	—
497	M₁₆	—	10	1	no	—
498	M₁₆	—	10	1	no	—
499	M₁₆	—	10	1	no	—
500	M₁₆	—	10	1	no	—
501	M₁₆	—	10	1	no	—
502	M₁₆	—	10	1	no	—
503	M₁₆	—	10	1	no	—
504	C₂×C₈	—	5	1	no	—
505	C₂×C₈	—	5	1	no	—
506	C₂×C₈	—	5	1	no	—
507	C₂×C₈	—	5	1	no	—
508	C₂×C₈	—	10	1	no	—
509	C₂×C₈	—	10	1	no	—
510	C₂×C₈	—	10	1	no	—
511	C₂×C₈	—	10	1	no	—
512	C₂×C₈	—	10	1	no	—
513	C₂×C₈	—	10	1	no	—
514	C₂×C₈	—	10	1	no	—
515	C₂×C₈	—	10	1	no	—
516	C₂×C₈	—	10	1	no	—
517	C₂×C₈	—	10	1	no	—
518	C₂×C₈	—	10	1	no	—
519	C₂×C₈	—	10	1	no	—
520	C₂×C₈	—	10	4	no	—
521	C₂×C₈	—	10	4	no	—
522	C₂×C₈	—	10	1	no	—
523	C₂×C₈	—	10	1	no	—
524	C₂×C₈	—	10	1	no	—
525	C₂×C₈	—	10	1	no	—
526	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
527	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
528	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
529	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
530	C₄⋊C₄	—	5	1	no	—
531	C₄⋊C₄	—	5	1	no	—
532	C₄⋊C₄	—	5	1	no	—
533	C₄⋊C₄	—	5	1	no	—
534	C₄⋊C₄	—	5	1	no	—
535	C₄⋊C₄	—	5	1	no	—
536	C₄⋊C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
537	C₄⋊C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
538	C₂²⋊C₄	—	5	1	no	—
539	C₂²⋊C₄	—	5	1	no	—
540	C₂²⋊C₄	—	5	1	no	—
541	C₂²⋊C₄	—	5	1	no	—
542	C₂²⋊C₄	—	5	1	no	—
543	C₂²⋊C₄	—	5	1	no	—
544	C₂²⋊C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
545	C₂²⋊C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
546	C₄²	—	5	1	no	—
547	C₄²	—	5	1	no	—
548	C₄²	—	5	1	no	—
549	C₄²	—	5	1	no	—
550	C₄²	—	5	1	no	—
551	C₄²	—	5	1	no	—
552	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
553	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
554	C₂×C₅	—	4	1	no	—
555	C₂×C₅	#2296	1	1	yes	characteristic
556	C₂×C₅	#2916	1	1	yes	characteristic
557	C₂×C₅	#2916	1	1	yes	characteristic
558	D₅	—	2	1	no	—
559	D₅	—	2	1	no	—
560	D₅	—	4	1	no	—
561	C₂³	—	5	1	no	—
562	C₂³	—	5	1	no	—
563	C₂³	—	10	1	no	—
564	C₂³	—	10	1	no	—
565	C₂³	—	20	1	no	—
566	C₂³	—	20	1	no	—
567	C₂³	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	5	1	no	—
571	C₂×C₄	—	5	1	no	—
572	C₂×C₄	—	5	1	no	—
573	C₂×C₄	—	5	1	no	—
574	C₂×C₄	—	5	1	no	—
575	C₂×C₄	—	5	1	no	—
576	C₂×C₄	—	5	1	no	—
577	C₂×C₄	—	5	1	no	—
578	C₂×C₄	—	5	1	no	—
579	C₂×C₄	—	5	1	no	—
580	C₂×C₄	—	10	1	no	—
581	C₂×C₄	—	10	1	no	—
582	C₂×C₄	—	10	1	no	—
583	C₂×C₄	—	10	1	no	—
584	C₂×C₄	—	10	1	no	—
585	C₂×C₄	—	10	1	no	—
586	C₂×C₄	—	10	1	no	—
587	C₂×C₄	—	10	1	no	—
588	C₂×C₄	—	20	1	no	—
589	C₂×C₄	—	20	1	no	—
590	C₂×C₄	—	20	1	no	—
591	C₂×C₄	—	20	1	no	—
592	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
593	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
594	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
595	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
596	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
597	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
598	C₈	—	2	1	no	—
599	C₈	—	2	1	no	—
600	C₈	—	2	1	no	—
601	C₈	—	2	1	no	—
602	C₈	—	10	2	no	—
603	C₈	—	10	2	no	—
604	C₈	—	10	2	no	—
605	C₈	—	10	2	no	—
606	C₈	—	10	1	no	—
607	C₈	—	10	1	no	—
608	C₈	—	10	1	no	—
609	C₈	—	10	1	no	—
610	C₈	—	20	1	no	—
611	C₈	—	20	1	no	—
612	C₈	—	20	1	no	—
613	C₈	—	20	1	no	—
614	C₅	#21372	1	1	yes	characteristic, complemented, Sylow
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	5	1	no	—
619	C₂²	—	5	1	no	—
620	C₂²	—	10	1	no	—
621	C₂²	—	10	1	no	—
622	C₂²	—	10	1	no	—
623	C₂²	—	10	1	no	—
624	C₂²	—	10	1	no	—
625	C₂²	—	40	1	no	—
626	C₂²	—	40	1	no	—
627	C₂²	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
628	C₄	—	2	1	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	5	1	no	—
634	C₄	—	5	1	no	—
635	C₄	—	10	1	no	—
636	C₄	—	10	1	no	—
637	C₄	—	10	1	no	—
638	C₄	—	10	1	no	—
639	C₄	—	10	1	no	—
640	C₄	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
641	C₄	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
642	C₂	—	4	1	no	—
643	C₂	—	10	1	no	—
644	C₂	—	10	1	no	—
645	C₂	—	20	1	no	—
646	C₂	#10617128	1	1	yes	characteristic
647	C₂	#10617418	1	1	yes	characteristic
648	C₂	#10617419	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊AGL(1,𝔽₅)
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₅×#433	C₄
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂³×D₅	C₂×Q₈
cosocle	C₂×C₄×D₅	C₂⁴
hypercenter	#433	AGL(1,𝔽₅)
hypocenter	C₅	#21372
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #117 ◁ #433

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #10604038	C₂	semidirect
5. #10604038	C₂	semidirect
6. #10604037	C₂	semidirect
7. #10604036	C₂	semidirect
12. #10603888	C₂	semidirect
13. #10603888	C₂	semidirect
14. C₄×#3996	C₂	semidirect
15. C₄×#3995	C₂	semidirect
614. C₅	#21372	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#10617110	2
#10617106	2
D₅×#433	2
#10604038	2
#10604037	2
#10604036	2
#10603918	2
#10603917	2
#10603916	2
#10603888	2
C₄×#3996	2
C₄×#3995	2
#21372	5